Try uncaching the chunk? I've not worked with AdvSearch so I'm not sure why it wouldn't grab the contents of the chunk but it's worth a try.
Infofar as using chunks in the content area, I'd say only do that if you will not be editing the chunk's content much, if ever. I do it when I want to prevent a client from editing the markup. Placing the table into a rich text TV for the client to edit is preferable if you do want them to be able to change it at all. To exclude it from any resource, simply leave the TV blank (no default), or you could create a separate template for that resource only and call up the TV. If you really want to use the same template as the other pages, you can use If or longhand conditionals in the template, although that will request to the database for every page and look for the condition (not ideal for every page).
i.e.
[[!If? &subject=`yourTV` &operator=`empty` &then=`` &else=`yourTV`]]
I'd lean towards just templating that page separately. Sometimes, it's simpler to do that than mess with conditions and try to use a single template everywhere.